In order to guarantee that \(\bar{Q}\)  may be physically acceptable in the dark sectors [1]}, we equal the right-hand sides of Eqs. (REF ) and
(REF ), which becomes
\(\frac{\mathrm {d R}}{\mathrm {d}z}=\frac{-\mathrm {R}}{(1+\mathrm {z})}\biggl ({\bar{\rm I}}_{\rm Q}(1+\mathrm {R})+3\mathrm {{\omega }_{DE}}\biggr ).\) 
